EIT Dynamics and Vibrations 4

Question 1

A spring-mass system has k = 400 N/m and m = 4 kg. What is the natural frequency in Hz?

Accepted Answer

1.59 Hz

Answer

ω_n = √(k/m) = √100 = 10 rad/s; f_n = ω_n/(2π) ≈ 1.59 Hz.

Question 2

A simple pendulum has a length of 1 m. What is its period of oscillation? (g = 9.81 m/s²)

Accepted Answer

2.0 s

Answer

T = 2π√(L/g) = 2π√(1/9.81) ≈ 2.01 s.

Question 3

Springs k₁ = 100 N/m and k₂ = 200 N/m are connected in series. What is the equivalent stiffness?

Accepted Answer

66.7 N/m

Answer

1/k_eq = 1/100 + 1/200 = 3/200, so k_eq = 200/3 ≈ 66.7 N/m.

Question 4

Springs k₁ = 150 N/m and k₂ = 250 N/m are connected in parallel. What is the equivalent stiffness?

Accepted Answer

400 N/m

Answer

Springs in parallel sum directly: k_eq = 150 + 250 = 400 N/m.

Question 5

What is the critical damping coefficient for a system with m = 2 kg and k = 200 N/m?

Accepted Answer

40 N·s/m

Answer

c_cr = 2√(mk) = 2√(2 × 200) = 2√400 = 40 N·s/m.

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